A multichannel digital receiver simultaneously down-converts a set of frequency division multiplexed (FDM) channels residing in a single sampled data signal stream. In a similar way, a multichannel digital transmitter simultaneously up-converts a number of baseband signals to assemble a set of FDM channels in a single sampled data signal stream. The polyphase filter bank has become the architecture of choice to efficiently accomplish these tasks. This architecture uses three interacting processes to assemble or to disassemble the channelized signal set. In a receiver these processes are an input commutator to effect spectral folding or aliasing due to a reduction in sample rate, a polyphase M-path filter to time align the partitioned and resampled time series in each path, and a discrete Fourier transform to phase align and separate the multiple base-band aliases. In a transmitter, these same processes operate in a related manner to alias baseband signals to high order Nyquist zones while increasing the sample rate with the output commutator. As such, multichannel wireless digital receivers and transmitters are defined by the relationships between channel bandwidth, channel separation and channel sample rate.